Bioeconomic modelling of a prey predator system using differential algebraic equations

Abstract

We propose a biological economic model based on prey-predator dynamics where the prey species are continuously harvested and predation is considered with type II functional response. The dynamic behavior of the proposed biological economic preypredator model is discussed. Continuous type gestational delay of predators is incorporated and its effect on the dynamical behavior of the model system is analyzed. Through considering delay as a bifurcation parameter, the occurrence of Hopf bifurcation of the proposed model system with positive economic profit is shown in the neighborhood of the co-existing equilibrium point. Finally, some numerical simulations are given to verify the analytical results and the system is analyzed through graphical illustrations.

Bifurcation and control of a bioeconomic model of a prey–predator system with a time delay

“…Moreover, the application of differential algebraic equations for the analysis of mathematical models based on biological theories is of great interest to researchers [15][16][17][18][19][20][21][22][23][24][25]. It may be noted that the most of the researchers analyzed the prey-predator dynamics using differential algebraic equations subject to the harvesting of the prey or predator population.…”

Optimal control of harvest and bifurcation of a prey–predator model with stage structure

“…It is observed that a numerous number of research articles proposed the population dynamics and analyzed the stability of the system in presence of harvesting effort and time delay but quite a few number of articles investigated the dynamical behavior of bioeconomic models using DAEs. Kar and Chakraborty [14] proposed a biological economic model based on prey-predator dynamics and found singularity induced bifurcation (SIB) phenomenon and impulsive behavior of the model system at the interior equilibrium point using DAEs. They have designed an optimal controller to eliminate singularity induced bifurcation and impulsive behavior of the model system when positive economic interest is taken into account.…”

Time delays and pollution in an open‐access fishery

“…Examples on more recent papers focusing on time delays in economic models are Keller (2010), Bianca et al (2013), and Gori et al (2018). In bioeconomics, several authors have analyzed the effects of absolute time delays both in single-population models and in predator-prey models (see, e.g., Bretschger & Smulders, 2018;Chakraborty et al, 2011Chakraborty et al, , 2012Ferrara et al, 2019;Gazi & Bandyopadhyay, 2008;Kar & Chakraborty, 2010;Martin & Ruan, 2001;Yuan et al, 2016;Q. Zhang et al, 2011;Y.…”